Find the mean, median and standard deviation for this sample. Round any decimals to three places.
data | 212 | 77 | 121 | 104 | 153 | 264 | 195 | 244 |
Solution:
x | x2 |
212 | 44944 |
77 | 5929 |
121 | 14641 |
104 | 10816 |
153 | 23409 |
264 | 69696 |
195 | 38025 |
244 | 59536 |
∑x=1370 | ∑x2=266996 |
Mean ˉx=∑xn
=212+77+121+104+153+264+195+244/8
=1370/8
=171.25
Median :
Observations in the ascending order are :
77,104,121,153,195,212,244,264
Here, n=8 is even.
M=Value of(n/2)thobservation+Value of(n2+1)thobservation2
=Value of(82)thobservation+Value of(82+1)thobservation2
=Value of4thobservation+Value of5thobservation2
=153+1952
=174
Sample Standard deviation S=√∑x2-(∑x)2nn-1
=√266996-(1370)28/7
=√266996-234612.5/7
=√32383.5/7
=√4626.2143
=68.0163
Sample Standard deviation =68.016
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